Prove that `alpha^(2)+beta^(2)=(alpha+beta)^(2)-2 alpha beta`

Find alpha^(2)+beta^(2)+alpha beta =?

If alpha & beta are any two complex numbers, prove that |alpha+beta|^2+|alpha-beta|^2=2(|alpha|^2+|beta|^2)

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

Prove that | alpha+sqrt(alpha^(2)-beta^(2))|+| alpha-sqrt(alpha^(2)-beta^(2))|=| alpha+beta|+| alpha-beta| where alpha,beta are complex numbers.

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha

Prove that, gammaalpha ^ (2), beta ^ (2), gamma ^ (2) beta + alpha, gamma + alpha, alpha + beta] | = (beta-gamma) (gamma-alpha) (alpha-beta) ( alpha + beta + gamma)

Prove that (cos alpha+cos beta)^(2)+(sin(alpha)+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

If cos(theta-alpha)=a,sin(theta-beta)=b, prove that a^(2)-2ab sin(alpha-beta)+b^(2)=cos^(2)(alpha-beta)

Prove that (cos alpha+cos beta)^(2)+(sin alpha+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

Prove that: | alpha beta gamma alpha^(2)beta^(2)gamma^(2)beta+gamma gamma+alpha alpha+beta|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)